Date: Jun 20, 2002 3:52 PM
Author: Guest
Subject: Trisection
Just wanted to share this, I worked it out a couple of years ago andwas surprised by the accuracy:

Near Exact Trisection:1. Start with an unknown angle &lt;90 deg., label the vertex A. 2. Draw an arc with origin at A crossing both lines of the angle atpoints B and C. 3. Draw line BC making an isosceles triangle.4. Using point C as the origin, draw an arc crossing line BC and theearlier arc somewhere between ¼ and ½ way between points C and B.Label where this new arc crosses line BC point D.Label where this new arc crosses the first arc point E.5. Draw line DE and extend it well past A . If line DE passesexactly through point A (it wont) stop, your first guess was an exacttrisection. 6. Extend line AC well past point A, step off 3 times length AC frompoint A and label the new point F.7. Swing an arc of length AF with A as the origin that crosses theextended line DE near point F.Label the intersection G.8. Draw line GA and extend it to intersect the original arc from step2.Label the intersection E.

Line AE is a good (within less than 1/1000 degree) trisection.However this is only the start. Repeating the process from step 4using CE as the arc radius results in a trisection to within 10E-11degrees. Each subsequent iteration improves the trisection by severalorders of magnitude.